Unified crystal plasticity model for fcc metals: From quasistatic to shock loading

Abstract

Mechanical response of metals is strongly dependent on the strain rate and exhibits drastic change as the strain rate varies across >10 orders of magnitude from quasistatic to shock loading. In this paper, we developed a unified crystal plasticity model for face-centered cubic (fcc) metals to describe the mechanical response in a wide range of strain rate from ${10}^{\ensuremath{-}5}$ to ${10}^{7}/\mathrm{s}$. The plasticity framework adopts the dislocation-based Orowan equation. Specifically, the mobility law for dislocation velocity incorporates both the thermal activation mechanism dominating at low strain rates and drag mechanism dominating at high strain rates, through a repeating waiting-running model. The rate dependence of total dislocation density (${\ensuremath{\rho}}_{t}$) evolution in the Orowan equation (implicitly) is captured by coupling the rate-dependent annihilation and the stress-dependent nucleation. More importantly, to capture the huge variation in mobile/total dislocation ratio ($f={\ensuremath{\rho}}_{m}/{\ensuremath{\rho}}_{t}$) at different strain rates, we propose a physics-based law for mobile dislocation fraction $f$ based on the exponential distribution of dislocation link lengths through a critical link length determined by the local stress. In addition, a thermohyperelastic model is supplemented to account for the nonlinear elastic behavior and thermoelastic coupling at shock loading. This unified model is validated against the mechanical response of single-crystal aluminum from quasistatic $(10{}^{\ensuremath{-}}5/\mathrm{s})$ to shock loading (${10}^{7}/\mathrm{s}$), where the features of thermal softening in static loading, thermal hardening in shock loading, and the strain-rate hardening in the medium strain-rate range are all quantitatively evaluated by a single set of parameters with a high average ${R}^{2}$ value of 0.93.